Direct Measurement of Steady-Shear Viscosity at High Shear Rates Using RPA

Inrtoduction

Characterizing flow behavior across a range of shear rates is imperative for optimization of industrial processing operations. Elevated shear rates are commonly linked to relevant manufacturing processes, such as pipe flow, molding, and extrusion. These measurements are critical for compounders, formulators, process engineers, and researchers for predicting material behavior and optimizing processing conditions. One of the most important properties for flow behavior is the measurement of viscosity as a function of shear rate, as this value is directly related to a compound’s processability and critical for optimizing processing conditions. The most common technique for measuring viscosity of a rubber compound is via capillary rheometry. Although practically ubiquitous in the rubber industry, capillary rheometer measurements require large sample volumes and extensive corrections for experimental factors such as wall slip and pressure gradients [1-3]. In addition, users cannot preserve the mechanical history of the compound before the actual testing as the samples need to be re-formed into cylindrical dimensions to fit into the capillary, which can lead to viscosity values that do not adequately represent the compound during processing.

Another alternative to viscosity measurements is utilizing steady-shear testing in an open boundary, rotational rheometer. Steady-shear testing applies a uni-directional deformation under a controlled shear rate over time. Highly elastic samples will often exhibit edge fracture often at low shear rates (< 0.1 s^-1), which limits the range of testing. One alternative approach to capture behavior at elevated shear rates, is to use the Cox-Merz relationship, which is an empirical relationship relating dynamic oscillatory data, such as that obtained from frequency sweeps, with steady-shear viscosity measurements. The Cox-Merz relationship (Figure 1) has been shown to correlate steady-shear viscosity with dynamic rheological data for many systems ranging from simple polymer melts to more complex polymer suspension systems [4-6].

However, the Cox-Merz relationship often fails for highly filled, elastic system due to weak filler-filler networks and complex interactions. As a result, the dynamic viscosity values derived using this relationship typically do not match the steady shear viscosity obtained with a capillary rheometer.

On the other hand, the TA Instruments RPA elite is uniquely poised to make steady-shear viscosity measurements of rubber compounds at elevated shear rates since it can apply a uni-directional rotation to the sample in a well-defined uniform shear flow field. Samples are compressed under high pressure forces and sealed in a biconical, serrated, closed-die system in an RPA, allowing users to perform steady-shear testing with increased sample grip and a delayed onset of edge fracture. It also allows users to precisely control the thermo-mechanical history of the sample with significantly lower sample volume compared to capillary rheometry measurements leading to improved precision. Lastly, the measurement can be coupled with additional RPA tests such as Payne effect tests, curing, frequency sweeps to obtain a wealth of information from a single experiment.

This application note demonstrates a facile method to directly measure the viscosity of rubber compounds using an RPA. These results are then compared to viscosity measurements using a capillary rheometer. This valuable information can further be used to understand the processing characteristics of a material, allowing operators to make adjustments in advance, thereby increasing productivity and reducing scrap.

Results and Discussion

The Cox-Merz relationship is an empirical relationship relating dynamic oscillatory data, such as that obtained from frequency sweeps, with steady-shear viscosity measurements. The Cox-Merz relationship has been shown to correlate steady-shear viscosity with dynamic rheological data for many systems ranging from simple polymer melts to more complex polymer suspension systems [4-6]. Figure 2 compares the viscosity derived from applying the Cox-Merz relationship to dynamic oscillation data (henceforth denoted as dynamic viscosity) to viscosity directly measured using capillary rheometry.

It can be observed that the dynamic viscosity and the capillary rheometry data do not overlap. The dynamic viscosity is shown to be dependent upon the applied strain in the oscillation tests. Lower viscosity values are observed for the dynamic test at 7% strain compared to 0.14% strain. This indicates a strong dependency of dynamic viscosity on the applied strain, which can be expected with filled rubber compounds, primarily due to the filler network and Payne effect [7]. A larger strain can break down the filler network, resulting in a less structured material that can flow easily. Interestingly, the viscosity obtained from both dynamic oscillatory tests do not match the viscosity obtained from a capillary rheometer. Since the filler networks are an important contributor to the rubber’s flow viscosity, it will be altered differently when the sample is subjected to an oscillatory deformation as compared to an uni-directional shear deformation on a capillary rheometer. The latter will typically cause an increased break down of the filler network. As a result, the viscosity measured using dynamic oscillatory testing will be much higher than the values obtained from a capillary rheometer, and the Cox-Merz relationship is not valid on such systems.

In order to overcome this gap, a new test method in the RPA has been employed to measure the steady state viscosity of rubber compounds. The RPA is programmed to apply a uni-directional deformation at a controlled shear rate is applied to the rubber sample, while measuring the resulting torque as a function of time. The torque reaches a plateau value as the material reaches steady state. Since the flow field is well-defined in the RPA, the torque can be easily converted to stress, and the viscosity can be calculated as the ratio of stress and shear rate. The viscosity of a generic tire tread compound can be seen in Figure 3 at shear rates of 0.01 to 10 s^-1.